Some Further Comments on the SCF Theory of the Excluded Volume Effect in Polymers

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Abstract
The self-consistent field approach to the excluded volume problem in a polymer chain is studied and discussed from the elementary point of view of statistical mechanics. First, true successive approximations to the self-consistent potential are derived from the corrected variation principle equation of Reiss. Second, the relationship between our basic self-consistent field equation previously derived and those derived by other routes, e.g., the Edwards equation and the Whittington hierarchy, is shown explicitly. Third, a uniform-expansion approximation is made in the potential of Edwards, and then a fifth-power-type equation for the expansion factor is obtained. A comparison of the result with those obtained previously and by Edwards provides an understanding of the effect of the uniform-expansion approximation.

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